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1. Is Bitcoin a Better
Portfolio Diversifier than
Gold? A copula and sectoral analysis for China
Prof. Wing Keung Wong
Asia University Taiwan
IRDF 2022, Universitas Muhammadiyah Yogyakarta
February, 8th 2022

2. Outlines
Introduction
01
Literature Review
02
Data and Methodology
03
Results and Discussions
04
Three Robustness Test
05
Conclusion
06

3. Introduction

4. Introduction
During the last years, Bitcoin and cryptocurrency have become increasingly
important in the financial system, not only as a payment tool but also as a financial
asset (Dyhrberg, 2016).
In China, there has been a prohibition from the government to trade
Bitcoin
Based on a survey of 100.000 individuals in China, the report
shows that Bitcoin has been considered as one of the ten
favorite investment assets of the middle class in China in 2018
while traders and exchanges try to find ways to bypass the
prohibition by moving the servers out of China
(2018 White Paper on the New Middle Class Survey –
By Prof Xiaobo Wu)

5. Fig 1. Investment assets by the New Middle Class in China in 2018
10%
Of new middle class in
China has been investing
in cryptocurrencies
In this list, goldalso appears as
one of the favorite investments in
China, as part of the precious metals
section. However, gold and
Bitcoin are profoundly different.
Gold is a real and physical asset and
was used as a real currency during
centuries under the gold standard.

6. Bitcoin
On the other hand, Bitcoin is a virtual and “young” asset, created in 2008 by a group of
programmers under the pseudonym Satoshi Nakamoto (Cheah and Fry, 2015).
Bitcoin is only a virtual money derived from mathematical
cryptography and conceived as an alternative to government-backed
currencies. It was originally envisaged that its construction and
digital “mining” processes would mean that Bitcoin prices should
be relatively stable.
Now, it is considered more as a speculative asset than a payment tool
(Horra, 2019). The price volatility and the potential for profit, together
with the prohibition, make investments in cryptocurrencies attractive and
desirable in China.

7. Study Objectives
the objective of our study is to test whether Bitcoin is really a profitable
investment for Chinese investors, who also invest in stocks and bonds (as
indicated in Figure 1).
Since the part of foreign assets invested by Chinese investors is very small (see
Figure 1), it is reasonably realistic to consider only Chinese stocks and bonds in the
present study.

8. Research Contribution
In addition to the use of a novel method to estimate the joint d
istribution function based on a copula,
our study also contributes to the literature by investigating the
specific case of China in which both Bitcoin and gold represe
nt specific asset classes
Furthermore, gold has an important cultural aspect in China
because it is used as gift in the new year and wedding seasons
(Cheng, 2014; Hoang et al., 2018b).
Thus, the comparison between these two different alternative
assets in Chinese stock and bond portfolios would provide
important information to Chinese investors and policy makers.

9. Literature Review

10. In this literature review, we present a
synthesis of recent studies about
Bitcoin, cryptocurrencies and their
relationship with traditional assets
such as stocks and bonds or with
other alternative assets such as gold.
We notice a huge increase of the number of studies on
Bitcoin and cryptocurrencies since 2015 and mostly from
2017 following the peak of Bitcoin prices on 18
December 2017 at $18,674.

11. 01 The behavior of Bitcoin and cryptocurrencies’ prices
02
The comparison between Bitcoin/cryptocurrencies and traditional assets
or other alternative assets (stocks, bonds, commodities, gold,
currencies, etc.);
03 The hedging ability of Bitcoin and cryptocurrencies in a diversified
portfolio;
04 The role of Bitcoin and cryptocurrencies in financial innovations,
payment systems and computer science
Academic studies on Bitcoin and cryptocurrencies
can be divided into four different groups

12. Some characteristics can be drawn, such as
speculative bubbles, informational inefficiency,
predictability, day-of-the-week effects,
interdependence of cryptocurrencies, high
volatility, dependence on investors’ sentiment,
dependence on some macroeconomic factors
and on other financial assets, etc.
Group 1 behavior of Bitcoin and cryptocurrencies’ prices

13. Group 2 The comparison between Bitcoin/cryptocurrencies and
traditional assets
Table 1 further shows that the volatility of Bitcoin is
higher than that of other assets such as gold, stocks, and
currencies. Moreover, Bitcoin has a low correlation with
traditional asset classes such as stocks, bonds,
commodities, and the USD.
In addition, this relation is asymmetric and nonlinear,
and cryptocurrencies can Granger cause commodity
futures.
Compared to gold, Bitcoin is a less efficient hedge and
safe haven asset for stocks.

14. As for the role of Bitcoin in the diversification of portfolios, which is directly related to our study, Group 3 in Table
1 shows that there have been inconclusive results regarding the ability of Bitcoin to be a hedge and a safe haven
asset.
Group 3 The hedging ability of Bitcoin and cryptocurrencies in a
diversified portfolio;
Dyhrberg (2016) found that Bitcoin can be used as a hedge against stocks in the
FTSE index and against the USD in the short run, like gold. However, Bouri et al.
(2017a) showed that Bitcoin is a poor hedge and is suitable for diversification
purposes only in portfolios composed of stocks, bonds, oil, commodities, and the
USD. On the other hand, Bouri et al. (2018b) found that Bitcoin can act as a safe
haven asset against the global financial stress. On the other hand, Akhtaruzzaman
et al. (2019) found that there is a lower dynamic conditional correlation between
Bitcoin and sectoral stocks and bonds. More importantly, the authors showed that
the Utilities sector has the most effective diversification benefit with Bitcoin.

15. Group 3 of Table 1, it has been shown that Bitcoin can be a
hedge and a safe haven for traditional assets, but this can be
time varying and depends on the country
(Borri, 2019a; Chan et al., 2013; Katjtazi and Moro, 2019; Shahzad et al., 2019).

16. Contributions
In this context, our study contributes to the existent literature on Bitcoin and cryptocurrencies in
different ways. First, we consider the specific case of China in which Bitcoin and
cryptocurrencies are forbidden by the government though it is one of the favorite investment
assets of the middle class in China (as mentioned in the Introduction).
Second, we consider the impact of the sector for stocks in China. To the best of our knowledge,
this has not been studied for China with Bitcoin while it has been proven to be important with
gold (e.g., Beckmann et al., 2017; Hoang et al., 2018a).
Third, we model the relationship between Bitcoin, and each considered asset (14 sectoral stock
indices, government bonds and corporate bonds) by simulating a joint distribution function of
returns based on the multivariate Student-t copula. To the best of our knowledge, this method
has not been used to measure the risk of portfolios diversified with Bitcoin. This method allows
us to evaluate the distribution of returns of considered portfolios appropriately and then to
measure the risk of loss on its left tail (with the Value-at-Risk and Expected Shortfall
measures). To this regard, the estimation of the joint distribution using the copula approach is
the main contribution of our study.

17. Data &
Methodology

18. The data set of this paper is
composed of 18 time-series
including Bitcoin prices, gold prices
for the Au9995 asset from the
Shanghai Gold Exchange, various
stock indexes and bond indexes
from the Shanghai Stock
Exchange from 20 July 2010 (the
first day Bitcoin quoted a price) to
30 April 2020.
Data
As shown in Table above, the price of all considered assets is
expressed in RMB, the local Chinese currency because we consider
the role of Bitcoin in Chinese portfolios for Chinese investors. However,
for Bitcoin prices, we first consider the USD because it is the reference
currency to express the Bitcoin price worldwide.

19. Descriptive
Statistics
it is found that Bitcoin has the highest return in
the 2010-2020 period (with an average of 115%
per year)
However, its volatility is
very high too, with a
standard deviation of
almost 101% annually.

20. Three Types of Portfolios
The first one (Type-1)
is composed of only
three assets which are
stocks, corporate
bonds, and government
bonds.
The second one (Type 2)
is composed of four assets
which are Bitcoin,
stocks, corporate bonds,
and government bonds.
The third one (Type-3)
is also composed of four
assets which are gold,
stocks, corporate bonds,
and government bonds.
The optimal weight of each asset is determined by the mean-CVaR optimization
method. Since there are 14 different sectoral stock indexes, the total number of
simulated portfolios is 42 portfolios (14 sectors * 3 types).

21. Methodology
Stochastic Dominance
we also consider the stochastic
dominance method to compare
the distributions of returns of
portfolios with and without Bitcoin
or gold, instead of only distortion
risk like in Ly et al. (2016)
Distortion Risk
provide the procedure to calculate the
risk of loss based on the left tail of the
portfolio’s return distribution
Monte Carlo simulation method
Calculate the integrals by providing
new algorithm based on the Monte
Carlo simulation method
Multivariate Student-t
copula
Use the multivariate
student-t copula instead of
bivariate copulas in Ly et
al (2016)
CVaR
Improve the portfolio optimization
procedure by minimizing the
conditional Value at Risk (CVaR)
instead of minimizing the variance
because the distribution of returns
is not normal
First Second Third Fourth Fifth

22. Result &
Discussions

23. Mean CVaR optimal portfolios
As mentioned above, we build optimal portfolios composed of four
assets Bitcoin (or gold), one sectoral stock index, corporate bonds,
and government bonds by minimizing their CVaR. The results are
presented in Table 4

24. Mean-CVaR results
From Table 4, for type-1 portfolios,
composed of stocks, corporate bonds,
and government bonds, we see that
most of the portfolios are composed of
stocks and government bonds with
about 49% on stocks and 43% on
government bonds, and a very small
part of corporate bonds.
This result is almost the same for all
the stock sectors.
Type-1 portfolios
Stock C_Bonds T_Bonds
Port. 1: Composite 0.492 0.062 0.436
Port. 2: Energy 0.49 0.46 0.04
Port. 3: Materials 0.492 0.482 0.016
Port. 4: Industrials 0.492 0.062 0.436
Port. 5:
Discretionary 0.492 0.482 0.016
Port. 6: Staples 0.492 0.482 0.016
Port. 7: Health care 0.492 0.482 0.016
Port. 8: Financials 0.492 0.062 0.436
Port. 9: Info. Tech. 0.492 0.482 0.016
Port. 10: Telecom 0.491 0.008 0.491
Port. 11: Utilities 0.492 0.482 0.016
Port. 12:
Commodity 0.492 0.482 0.016
Port. 13: A-shares 0.492 0.062 0.436
Port. 14: B-shares 0.492 0.062 0.436

25. Mean-CVaR results
Type-2 portfolios
Bitcoin Stock C_Bonds T_Bonds
Port. 1: Composite 0.044 0.464 0.476 0.024
Port. 2: Energy 0.042 0.456 0.424 0.068
Port. 3: Materials 0.054 0.458 0.374 0.120
Port. 4: Industrials 0.076 0.430 0.440 0.046
Port. 5: Discretionary 0.056 0.482 0.428 0.034
Port. 6: Staples 0.040 0.469 0.332 0.156
Port. 7: Health care 0.029 0.462 0.072 0.428
Port. 8: Financials 0.040 0.462 0.308 0.182
Port. 9: Info. Tech. 0.044 0.460 0.014 0.486
Port. 10: Telecom 0.076 0.426 0.434 0.058
Port. 11: Utilities 0.026 0.474 0.484 0.006
Port. 12: Commodity 0.082 0.414 0.014 0.486
Port. 13: A-shares 0.044 0.464 0.476 0.024
Port. 14: B-shares 0.074 0.424 0.486 0.010
For portfolios of type 2, including also
Bitcoin, we see that the part of
Bitcoin in optimal portfolios is very
small, less than 1%.
This result means that to minimize
the CVaR of optimal portfolios,
it should be included a very small
portion of Bitcoin.

26. Mean-CVaR results
Type-3 portfolios
Gold Stock C_Bonds T_Bonds
Port. 1: Composite 0.364 0.148 0.394 0.090
Port. 2: Energy 0.396 0.114 0.168 0.330
Port. 3: Materials 0.438 0.068 0.306 0.186
Port. 4: Industrials 0.373 0.123 0.148 0.348
Port. 5: Discretionary
0.416 0.086 0.438 0.058
Port. 6: Staples 0.336 0.164 0.492 0.000
Port. 7: Health care 0.401 0.090 0.338 0.162
Port. 8: Financials 0.362 0.142 0.012 0.478
Port. 9: Info. Tech. 0.416 0.080 0.179 0.320
Port. 10: Telecom 0.390 0.116 0.096 0.404
Port. 11: Utilities 0.354 0.142 0.210 0.286
Port. 12: Commodity 0.432 0.082 0.094 0.394
Port. 13: A-shares 0.364 0.148 0.394 0.090
Port. 14: B-shares 0.404 0.090 0.318 0.180
For portfolios of type 3, show that
optimal weight of gold in mean-
CVaR optimal portfolios is much
higher than that of Bitcoin, with a
value between 36% and 43%.
This result means that gold is a better
component in Chinese portfolios to minimize the
potential loss which is measured by the CVaR.
We also note that when gold is included, the
proportion of corporate bonds also becomes
higher than in type-1 portfolios, like with Bitcoin.
This result suggests that corporate bonds are
more suitable when being diversified with
alternative assets like Bitcoin and gold.

27. To summarize, Table 4 informs us that the optimal weight of Bitcoin in mean-CVaR
portfolios is very low, less than 1%, while the optimal weight of gold in mean-CVaR
portfolios is much higher, between 30% and 40%.
This high weight of gold in Chinese optimal portfolios confirms the result obtained by
Beckmann et al. (2017) who also investigated the role of gold in sectoral stocks in China.
Furthermore, we also note that corporate bonds are more suitable than government bonds
when being diversified with alternative assets like Bitcoin and gold. This result may be
explained by the fact that corporate bonds reflect dynamics of corporations and are thus more
suitable to volatile markets like those of Bitcoin and gold.

28. Dependence
structure
with copulas
As explained in Section 3, the multivariate Student-t copula is
used to describe the multivariate dependence structure among
Bitcoin/Gold and traditional assets in China such as stocks
and bonds.
Table 5 presents the results for Bitcoin while Table 6 presents
the results for Gold.

29. Table 5: Copula
dependence
structure for
portfolios with
Bitcoin
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From Table 5, we note that
Bitcoin has a positive and low
correlation with stocks, while it
has a negative correlation with
corporate and government
bonds.
Copula (Bitcoin USD)
Type of
copula Parameter 1 (correlation matrix)
Parameter 2
(degree of
freedom)
Bitcoin + Composite +
C_Bonds + T_Bonds
Student
-t
[[0.0340 -0.0391 -0.0261 0.0559
0.0046 0.3099]] 13.077
Bitcoin + Energy + C_Bonds +
T_Bonds
Student
-t
[[0.0231 -0.0372 -0.0268 0.0269 -
0.0085 0.3099]] 12.09
Bitcoin + Materials + C_Bonds
+ T_Bonds
Student
-t
[[0.0402 -0.0377 -0.0255 0.0620 -
0.0001 0.3098]] 13.013
Bitcoin + Industrials +
C_Bonds + T_Bonds
Student
-t
[[0.0247 -0.0387 -0.0267 0.0548
0.0169 0.3096]] 13.222
Bitcoin + Discretionary +
C_Bonds + T_Bonds
Student
-t
[[0.0360 -0.0395 -0.0257 0.0514
0.0069 0.3115]] 12.334
Bitcoin + Staples + C_Bonds
+ T_Bonds
Student
-t
[[0.0343 -0.0386 -0.0268 0.0606
0.0110 0.3091]] 14.32
Bitcoin + Health care +
C_Bonds + T_Bonds
Student
-t
[[0.0261 -0.0407 -0.0252 0.0694
0.0185 0.3104]] 14.415
Bitcoin + Financials +
C_Bonds + T_Bonds
Student
-t
[[0.0079 -0.0408 -0.0271 0.0232 -
0.0153 0.3081]] 12.08
Bitcoin + Info. Tech. +
C_Bonds + T_Bonds
Student
-t
[[0.0504 -0.0391 -0.0245 0.0551
0.0086 0.3102]] 14.164
Bitcoin + Telecom + C_Bonds
+ T_Bonds
Student
-t
[[0.0403 -0.0394 -0.0256 0.0596
0.0104 0.3092]] 16.769
Bitcoin + Utilities + C_Bonds
+ T_Bonds
Student
-t
[[0.0308 -0.0395 -0.0257 0.0701
0.0248 0.3103]] 13.382
Bitcoin + Commodity +
C_Bonds + T_Bonds
Student
-t
[[0.0376 -0.0368 -0.0255 0.0462 -
0.0093 0.3099]] 12.44
Bitcoin + A-shares + C_Bonds
+ T_Bonds
Student
-t
[[0.0338 -0.0391 -0.0261 0.0559
0.0047 0.3099]] 13.06
Bitcoin + B-shares + C_Bonds
+ T_Bonds
Student
-t
[[0.0407 -0.0386 -0.0264 0.0314 -
0.0246 0.3091]]
13.188

30. Table 6: Copula
dependence
structure for
portfolios with gold
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Regarding gold, Table 6 shows that the
correlation between gold and sectoral
stocks is lower than that with Bitcoin.
In some cases, the correlation between
gold and stocks is even negative, such
as with stocks of the Utilities and B-
Shares sectors.
Copula (gold)
Type of
copula Parameter 1 (covariance matrix)
Parameter 2
(degree of
freedom)
Gold + Composite + C_Bonds +
T_Bonds
Student
-t
[[0.0381 -0.0022 0.0447 0.0543
0.0055 0.3100]] 9.154
Gold + Energy + C_Bonds +
T_Bonds
Student
-t
[[0.0668 -0.0009 0.0454 0.0254 -
0.0082 0.3096]] 9.045
Gold + Materials + C_Bonds +
T_Bonds
Student
-t
[[0.1300 0.0001 0.0468 0.0610 0.0007
0.3094]] 9.824
Gold + Industrials + C_Bonds +
T_Bonds
Student
-t
[[0.0203 -0.0024 0.0460 0.0523
0.0156 0.3098]] 9.09
Gold + Discretionary + C_Bonds
+ T_Bonds
Student
-t
[[0.0269 -0.0026 0.0444 0.0491
0.0083 0.3118]] 8.968
Gold + Staples + C_Bonds +
T_Bonds
Student
-t
[[0.0118 -0.0029 0.0447 0.0588
0.0132 0.3094]] 10.821
Gold + Health care + C_Bonds +
T_Bonds
Student
-t
[[0.0039 -0.0029 0.0445 0.0664
0.0188 0.3111]] 10.813
Gold + Financials + C_Bonds +
T_Bonds
Student
-t
[[0.0225 -0.0022 0.0458 0.0228 -
0.0140 0.3077]] 8.606
Gold + Info. Tech. C_Bonds +
T_Bonds
Student
-t
[[0.0100 -0.0001 0.0450 0.0524
0.0088 0.3111]] 10.102
Gold + Telecom + C_Bonds +
T_Bonds
Student
-t
[[0.0060 -0.0022 0.0448 0.0600
0.0137 0.3108]] 10.824
Gold + Utilities + C_Bonds +
T_Bonds
Student
-t
[[-0.0031 -0.0011 0.0460 0.0681
0.0262 0.3109]] 9.182
Gold + Commodity+ C_Bonds +
T_Bonds
Student
-t
[[0.1458 0.0003 0.0457 0.0442 -
0.0080 0.3095]] 9.567
Gold + A-shares + C_Bonds +
T_Bonds
Student
-t
[[0.0383 -0.0022 0.0447 0.0543
0.0055 0.3100]] 9.146

31. Distortion risk results
Results in Table 7 show that including gold in Chinese portfolios is helpful to reduce
the risk of loss (measured by VaR and ES) and reduce the volatility risk (measured by
the standard deviation). However, including Bitcoin in Chinese portfolios produces the
reverse: Bitcoin does not help reduce the risk but helps increase the return.
This result suggests that gold is more relevant to risk-averse investors whose objective
is to invest in lower-risk portfolios. On the other hand, Bitcoin is more relevant to risk-
seeking investors whose objective is to invest in higher-risk portfolios (Hoang et al.,
2015a). As we mentioned in the Introduction, most of Chinese investors are risk averse.

32. Risk
measur
es
1.
Composit
e
Port. 1 –
S.
Port. 1 –
B
Port. 1 –
G 2. Energy
Port. 2 –
S.
Port. 2 -
B
Port. 2 -
G
3.
Materials
Port. 3 –
S
Port. 3 -
B
Port. 3 -
G
VaR 1% -5.731 -2.805 -2.606 -1.612 -6.414 -3.128 -2.910 -1.730 -6.578 -3.220 -3.007 -1.956
VaR 5% -2.324 -1.135 -1.155 -0.619 -2.823 -1.373 -1.352 -0.669 -3.000 -1.466 -1.471 -0.676
ES 1% -5.731 -2.805 -2.606 -1.612 -6.414 -3.128 -2.910 -1.730 -6.578 -3.220 -3.007 -1.956
ES 5% -5.079 -2.480 -2.269 -1.218 -5.268 -2.566 -2.425 -1.309 -5.697 -2.785 -2.587 -1.395
Mean 0.005 0.010 0.033 0.016 -0.033 -0.006 0.014 0.011 -0.002 0.009 0.034 0.016
SD 1.317 0.648 0.681 0.388 1.662 0.815 0.811 0.415 1.729 0.852 0.874 0.427
Sharpe 0.366 1.546 4.845 4.101 -2.007 -0.731 1.748 2.537 -0.126 1.108 3.842 3.668
Risk
measur
es
4.
Industrials
Port. 4 –
S. Port. 4 - B
Port. 4 -
G
5.
Discretionar
y
Port. 5 –
S.
Port. 5 -
B
Port. 5 -
G 6. Staples
Port. 6 –
S.
Port. 6 -
B
Port. 6 -
G
VaR 1% -6.557 -3.208 -2.962 -1.623 -6.009 -2.936 -2.923 -1.845 -5.325 -2.602 -2.518 -1.468
VaR 5% -2.699 -1.320 -1.383 -0.632 -2.748 -1.341 -1.435 -0.632 -2.580 -1.259 -1.272 -0.632
ES 1% -6.557 -3.208 -2.962 -1.623 -6.009 -2.936 -2.923 -1.845 -5.325 -2.602 -2.518 -1.468
ES 5% -5.407 -2.642 -2.455 -1.241 -5.295 -2.583 -2.546 -1.276 -4.615 -2.250 -2.177 -1.160
Mean 0.001 0.008 0.045 0.014 0.000 0.010 0.035 0.016 0.044 0.032 0.048 0.023
SD 1.596 0.786 0.851 0.394 1.562 0.769 0.845 0.404 1.515 0.746 0.765 0.397
Sharpe 0.047 1.021 5.333 3.537 -0.030 1.335 4.164 4.057 2.881 4.284 6.308 5.720
Risk
measur
es
7. Health
care
Port. 7 –
S. Port. 7 - B
Port. 7 -
G
8.
Financials
Port. 8 –
S.
Port. 8 -
B
Port. 8 -
G
9. Info.
Tech.
Port. 9 –
S.
Port. 9 -
B
Port. 9 -
G
VaR 1% -5.575 -2.726 -2.542 -1.764 -5.771 -2.823 -2.661 -1.671 -6.269 -3.068 -2.900 -1.795
VaR 5% -2.699 -1.318 -1.271 -0.612 -2.374 -1.158 -1.142 -0.627 -3.413 -1.668 -1.626 -0.649
ES 1% -5.575 -2.726 -2.542 -1.764 -5.771 -2.823 -2.661 -1.671 -6.472 -3.190 -3.299 -1.795
ES 5% -4.770 -2.328 -2.181 -1.219 -3.992 -1.940 -1.850 -1.206 -5.453 -2.665 -2.513 -1.290

33. Risk
measures 10. Telecom Port. 10– S. Port.10 - B Port.10 - G 11. Utilities Port. 11 – S. Port.11- B Port.11- G
12.
Commodity Port. 12–S Port.12 - B Port.12- G
VaR 1% -6.964 -3.403 -3.142 -1.689 -6.151 -3.009 -2.832 -1.557 -6.295 -3.082 -3.118 -1.925
VaR 5% -3.415 -1.668 -1.631 -0.677 -2.360 -1.152 -1.143 -0.603 -2.938 -1.435 -1.456 -0.690
ES 1% -6.964 -3.403 -3.142 -1.689 -6.151 -3.009 -2.832 -1.557 -6.295 -3.082 -3.118 -1.925
ES 5% -6.139 -2.997 -2.714 -1.323 -5.164 -2.520 -2.387 -1.186 -5.432 -2.656 -2.575 -1.400
Mean 0.019 0.017 0.053 0.016 0.001 0.011 0.023 0.014 -0.018 0.001 0.038 0.013
SD 1.951 0.958 0.979 0.419 1.376 0.679 0.680 0.376 1.691 0.833 0.892 0.433
Sharpe 0.997 1.759 5.456 3.829 0.051 1.599 3.341 3.738 -1.090 0.173 4.205 2.941
Risk
measures 13. A-shares Port.13 – S. Port.13 - B Port.13 - G 14. B-shares Port. 14 – S. Port.14- B Port.14- G C.-Bonds T.-Bonds Bitcoin Gold
VaR 1% -5.730 -2.804 -2.606 -1.611 -7.291 -3.566 -3.135 -1.867 -0.147 -0.289 -37.419 -4.535
VaR 5% -2.325 -1.135 -1.155 -0.619 -2.422 -1.182 -1.281 -0.617 -0.028 -0.028 -8.829 -1.441
ES 1% -5.730 -2.804 -2.606 -1.611 -7.291 -3.566 -3.135 -1.867 -0.147 -0.289 -37.419 -4.535
ES 5% -5.078 -2.479 -2.268 -1.218 -5.820 -2.840 -2.594 -1.331 -0.028 -0.028 -11.424 -3.033
Mean 0.005 0.010 0.033 0.016 -0.001 0.007 0.044 0.015 0.021 0.015 0.461 0.015
SD 1.318 0.649 0.681 0.388 1.430 0.703 0.782 0.389 0.037 0.041 6.434 0.910
Sharpe 0.366 1.546 4.843 4.100 -0.070 1.018 5.652 3.952 56.980 35.541 7.160 1.657

34. Stochastic dominance results
In this sub-section, we present the results obtained with the stochastic dominance method.
The objective is to compare the return distributions of the three types of portfolios
considered. The results for the four stochastic dominance orders are presented in Table 8.
Overall, Table 8 shows that for 8
sectors over 14, type-1 portfolios
dominate type-2 portfolios, while
for the 6 other sectors, type-1
portfolios are dominated by type-
2 portfolios. This result means that
in most cases, portfolios without
Bitcoin dominate those with
Bitcoin.
Regarding gold, Table 8 shows that in
all cases, portfolios with gold
dominate portfolios without gold
(type-1 portfolios are dominated by
type-3 portfolios for all sectors).
Regarding the stochastic dominance
comparison between portfolios
including Bitcoin and those including
gold,

35. To conclude, the results from the
whole period (2010-2020) show that
gold is a better portfolio diversifier
than Bitcoin because it helps better
reduce the risk. However, Bitcoin
can also be considered as a good
portfolio considering that it helps
increase the return.
From this finding, we conclude that gold is
more suitable to risk-averse investors while
Bitcoin is more suitable to risk-seeking
investors. However, the above results are
valid for the whole period and for daily data.
Then, one can wonder whether these results
still hold if we consider other periods or other
data frequencies

36. 3 Robustness
Check
Robustness Tests

37. Robustness-check 1: Sub-period analysis
For the first robustness check, we divide the whole period (2010-2020) into two sub-periods. The first one
spreads from 2010 to 2015, during which the price of Bitcoin was low and stable (see Figure 2).
The second one spreads from 2016 to 2020 during which there were high prices and high volatility for
Bitcoin.
First, the weights of both Bitcoin and gold in the optimal portfolios change over time and is higher in sub-
period 2 than in sub-period 1. Second, the dependence structure also changes over time due to the variation
of the value of the parameters of the multivariate Student-t copula. Third, the risk of loss is lower in sub-
period 2 than in sub-period 1. Fourth, the Sharpe ratio is higher for portfolios with Bitcoin than for those
with gold in most of cases only in the first sub-period.
These results thus show the time-varying character of the portfolio diversification between traditional assets
and alternative assets such as Bitcoin and gold. However, this robustness check allows us to confirm the
finding for the whole period because gold remains to be more relevant to risk-averse investors while
Bitcoin remains to be more relevant to risk-seeking investors in both sub-periods 1 and 2.
So, we conclude that this finding is robust.

38. Robustness-check 2: Monthly analysis
The second robustness check consists of
comparing between daily and monthly results
over the same period from 2010 to 2020.
The objective is to see whether the data
frequency has an impact on the results. This
robustness check also allows us to see whether
the investment horizon (daily or monthly in
this case) can have an impact on the portfolio
diversification using Bitcoin or gold.
The results show that the time
frequency has an impact on the weight
of Bitcoin or gold in optimal portfolios.
It also has impacts on the dependence
structure between the traditional and
alternative assets and on the risk of loss
of the portfolios. However, we still find
that Bitcoin is more relevant to risk-
seeking investors while gold is more
relevant to risk-averse investors.

39. Robustness-check 3: Does the currency of Bitcoin prices matter?
In this sub-section, we convert Bitcoin
prices into the RMB, while the previous
results are obtained with Bitcoin prices in
the USD, to see whether the currency can
impact our main findings. The results still
show that the finding following which
Bitcoin is more relevant to risk-seeking
investors and gold is more relevant to risk-
averse investors is robust to the change of
the currency of Bitcoin prices (from USD to
RMB).
Finally, the three above robustness
checks show that the results about the
optimal weight of Bitcoin or gold, the
dependence structure and the distortion
risk values can be sensitive to time,
frequency and currency.
However, the conclusion that Bitcoin is
more relevant to risk-seeking investors and
gold is more relevant to risk-averse
investors remains robust.

40. Conclusion

41. Conclusions
• We conclude that gold is more relevant to risk-averse investors (with lower risk and
higher return) while Bitcoin is more relevant to risk-seeking investors (with much higher
risk and much higher return).
• In this context, we conclude that gold is more relevant to Chinese investors. Regarding the
risk, it is important to note that in most cases, the Value at Risk and Expected Shortfall are
about -3% for portfolios with Bitcoin and about -1.5% for portfolios with gold, knowing that
those for non-diversified portfolios are about -3.5%.
• Furthermore, the stochastic dominance results show that portfolios diversified by gold
dominate portfolios diversified by Bitcoin. This result once again demonstrates that gold is
more suitable to risk-averse investors while Bitcoin is more suitable to risk-seeking investors.
Finally, three robustness tests show that this finding is robust to time, data frequency, and the
currency of Bitcoin prices (in USD or in RMB).

42. Conclusions
Overall, we conclude that Bitcoin is a better portfolio diversifier in Chinese portfolios for risk
seekers while gold is a better portfolio diversifier for risk-averse investors.
• The prohibition to trade Bitcoin may support the illusion of an even higher potential to the investors
while the result of our research shows that gold is indeed more appropriate to Chinese investors
because most of them are risk-averse (according to the survey of Xiaobo Wu in 2018).
• Though its risky aspect, Bitcoin has been one of the favorite investment assets of the new middle
class in China. May this irrationality be explained by behavioral aspects?
• For future studies, we suggest investigating the relationship between investors’ sentiments,
measured by various proxies such as VIX, Tweets, Google Search, surveys, etc., and the dynamics of
Bitcoin prices, especially during the Covid-19 pandemic.

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